Remarks on the Maximum Correlation Coefficient
Amir Dembo, Abram Meerovich Kagan, Lawrence A. Shepp · Bernoulli · 2001
The maximum correlation coefficient between partial sums of independent and identically distributed random variables with finite second moment equals the classical (Pearson) correlation coefficient between the sums, and thus does not depend on the distribution of the random variables. This result is proved, and relations between the linearity of regression of each of two random variables on the other and the maximum correlation coefficient are discussed.